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  • Textbook
  • © 2013

Space-Filling Curves

An Introduction with Applications in Scientific Computing

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  • Connects the different techniques to describe space-filling curves to corresponding algorithms

  • Connects space-filling curves and respective orders to regular and adaptive meshes for discretisation

  • Describes parallelisation and cache-efficient algorithms based on space-filling curves

  • Provides a section on references to both pioneering and current research on space-filling curves in scientific computing?

  • Includes supplementary material: sn.pub/extras

Part of the book series: Texts in Computational Science and Engineering (TCSE, volume 9)

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  • ISBN: 978-3-642-31046-1
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Table of contents (15 chapters)

  1. Front Matter

    Pages i-xiii
  2. How to Construct Space-Filling Curves

    • Michael Bader
    Pages 15-30
  3. Approximating Polygons

    • Michael Bader
    Pages 67-76
  4. Sierpinski Curves

    • Michael Bader
    Pages 77-91
  5. Further Space-Filling Curves

    • Michael Bader
    Pages 93-108
  6. Space-Filling Curves in 3D

    • Michael Bader
    Pages 109-127
  7. Refinement Trees and Space-Filling Curves

    • Michael Bader
    Pages 129-142
  8. Parallelisation with Space-Filling Curves

    • Michael Bader
    Pages 143-165
  9. Locality Properties of Space-Filling Curves

    • Michael Bader
    Pages 167-180
  10. Back Matter

    Pages 239-278

About this book

­The present book provides an introduction to using space-filling curves (SFC) as tools in scientific computing. Special focus is laid on the representation of SFC and on resulting algorithms. For example, grammar-based techniques are introduced for traversals of Cartesian and octree-type meshes, and arithmetisation of SFC is explained to compute SFC mappings and indexings.

­The locality properties of SFC are discussed in detail, together with their importance for algorithms. Templates for parallelisation and cache-efficient algorithms are presented to reflect the most important applications of SFC in scientific computing. Special attention is also given to the interplay of adaptive mesh refinement and SFC, including the structured refinement of triangular and tetrahedral grids. For each topic, a short overview is given on the most important publications and recent research activities.

Keywords

  • Hilbert curve, Peano curve, Sierpinski curve
  • adaptive meshes
  • algorithms in scientific computing
  • octrees
  • parallelisation
  • space-filling curves

Reviews

From the reviews:

“This book concentrates on low-dimensional, two or three at most, curves used for linearly ordering points on the 2D or 3D grid with applications in computer graphics and data structures. … Each section ends with indications for further reading and exercises. This is a new book in the field of computer science which should be a valuable resource for advanced undergraduate and graduate students as well as more experienced researchers.” (Ewa Skubalska-Rafajłowicz, Mathematical Reviews, January, 2014)

“Bader’s book … provides an introduction to the algorithmics of space-filling curves. … The book has many color illustrations and can be used as a textbook and as reference monograph for research.” (Luiz Henrique de Figueiredo, MAA Reviews, April, 2013)

“This is a gentle introduction to space filling curves. Emphasis is on the representation, implementation and application in computer science. … It is clear that the author has a long teaching experience with this subject. He had found the right balance between motivation, rigor, application, implementation, in just the right pace to take the reader/student along climbing up the hill towards of increasing complexity as academic examples are left and one approaches the real life applications.” (A. Bultheel, The European Mathematical Society, December, 2012)

Authors and Affiliations

  • , Department of Informatics, Munich Center of Advanced Computing, Garching, Germany

    Michael Bader

About the author

Michael Bader is professor for computer science at Technische Universität München, where he leads a research group on hardware-aware algorithms and software for high performance computing (located at the Leibniz Supercomputing Centre). His focus in research and teaching is on algorithmic challenges imposed by modern
computing platforms. A large part of his work is dedicated to exploiting locality properties of space-filling curves for simulation tasks in science and engineering.



Bibliographic Information

Buying options

eBook
USD 29.99 USD 84.99
65% discount Price excludes VAT (USA)
  • ISBN: 978-3-642-31046-1
  • Instant PDF download
  • Readable on all devices
  • Own it forever
  • Exclusive offer for individuals only
  • Tax calculation will be finalised during checkout
Softcover Book
USD 37.99 USD 109.99
65% discount Price excludes VAT (USA)
Hardcover Book
USD 54.99 USD 109.99
50% discount Price excludes VAT (USA)